Statistical analysis was applied to optimize the electrochemical mineralization of ibuprofen with two boron-doped diamond (BDD) electrodes in a continuous electrochemical flow reactor under recirculation batch mode. A central composite rotatable (CCR) experimental design was used to analyze the effect of initial pH (2.95–13.04), current intensity (2.66–4.34 A), and volumetric flow rate (0.16–1.84 L/min) and further optimized by response surface methodology (RSM) to obtain the maximum mineralization efficiency and the minimum specific energy consumption. A 91.6% mineralization efficiency (E_M) of ibuprofen with a specific energy consumption (E_C) of 4.36 KW h/g TOC within 7 h of treatment was achieved using the optimized operating parameters (pH₀ = 12.29, I = 3.26 A, and Q of 1 L/min). Experimental results of RSM were fitted via a third-degree polynomial regression equation having the performance index determination coefficients (R²) of 0.8658 and 0.8468 for the E_M and E_C, respectively. The reduced root-mean-square error (RMSE) was 0.1038 and 0.1918 for E_M and E_C, respectively. This indicates an efficient predictive performance to optimize the operating parameters of the electrochemical flow reactor with desirability of 0.9999993. Besides, it was concluded that the optimized conditions allow to achieve a high percentage of ibuprofen mineralization (91.6%) and a cost of 0.002 USD $/L. Therefore, the assessed process is efficient for wastewater remediation.”

Effectiveness factors have great relevance in multiphase reactors modeling since they are the conventional way of incorporating the effects of intra-particle resistance reaction rate. This work determines the description level effect of catalytic pellet microstructure on mass and energy effective transport coefficients prediction, isothermal and no isothermal. For such a purpose some results about on evaluation of the effective diffusivity and conductivity with the methodology of volume averaging were applied. The obtained results along with a Langmuir–Hinshelwood/Hougen–Watson kinetic expression were applied to establish the concentration and temperature fields in a catalytic particle. The evaluation of concentration field and effectiveness factors were developed using two different models: pseudo- homogeneous mass and energy transport model for a catalytic particle with reaction in all domain, and heterogeneous mass and energy transport model with fluid-catalytic surface interphase reaction for a realistic porous structure model. The results show the differences in concentration and temperature profiles between both models and consequently in effectiveness factors. This could be ascribed to the form of evaluation of effective transport coefficients used in the pseudo-homogeneous model, and presumably to the simple shape of the unit cells used for the solution of the closure problem for the average transport equations with homogeneous reaction.

2-Chlorophenol (2-CP) is a dangerous organic contaminant found in wastewater. In this work, 2.5 L of a 2-CP solution (1 mol/m³) was electrochemically treated in a flow-by reactor equipped with two boron-doped diamond electrodes (BDD) under batch recirculation mode for a period for 4 h, a current density of 0.14 A/cm², a volumetric flow rate of 1 L/min, and pH = 7.3. In this work, a parametric mathematical model of the degradation efficiency of 2-CP was developed using an axial dispersion model and a continuous stirred tank for the flow-by reactor (FBR), which was constructed using a shell mass balance considering the dispersion and convection terms and the reservoir tank (CST), which was constructed using a mass balance of 2-CP. The parametric mathematic model of the electrochemical degradation of 2-chlorophenol was numerically resolved by employing the software package COMSOL Multiphysics^® V. 5.3, where a mass transfer equation for diluted species and a global differential equation represents the FBR and CST, respectively. The results indicate that the parametric mathematical model proposed in this research fits the experimental results, and this is supported by the index performance values such as the determination coefficient (R² = 0.9831), the mean square error (MSE = 0.0307), and the reduced root-mean-square error (RMSE = 0.1754). Moreover, the degradation efficiency of 2-CP estimated by the proposed model achieves 99.06%, whereas the experimental degradation efficiency reached 99.99%, a comparative error of 0.93%. This corroborates the predictive ability of the developed mathematical model and the effectiveness of the employed electrooxidation process. Finally, a 0.143 USD/L total operating cost for the electrochemical plant was estimated.

Many of the engineering problems have multiphysics and multiscale nature. Non-isothermal flows, stirred reactors, turbulent mixing and membrane filtration, are prevalent cases in which the coupling of several physics phenomena is required for the adequate prediction of overall behaviors. Also, a multiscale analysis, where the same phenomenon is analyzed at different scales, can lead to better understanding of the phenomena, which can be used in optimization and to provide adequate scale-up methodologies. Studies incorporating both multiscale and multiphysics analysis are rarely addressed in literature; in fact, these kinds of problems will be the research challenge in the next years. Computer fluid dynamics (CFD) techniques have shown to be promising to deal with these kinds of systems. In this chapter, these are used to implement a multiscale analysis of the hydrodesulphurization (HDS) process for light gas-oil (LGO). The aforementioned is carried out by the analysis of mass an energy transport at: (1) microporous (MP) scale, (2) pseudo-homogeneous catalyst (PHC) scale, and by analysis of (3) momentum and mass transport at reactor scale (RS). In addition, a particular discussion is made regarding the proper establishment of the model, its validation, the use of different boundary conditions, its justification; and the dependence of solutions of parameters and initial and boundary conditions.